Electromechanical calculator



c1. E. SMITH ELEGTRO-MECHANICAL CALCULATOR Filed Oct. 29, 1942 3Sheets-Sheet 1 INVENTOR. QMQ C. W

Mm I ith April 1, WM. c. E. SMITH ELECTRO-MECHANICAL CALCULATOR FiledOct. 29, 1942 5 Sheets-Sheet 2 INVENTOR. CwJZ swam Q+ M M M mil 1, 194?.c. E. SMITH 2,418,238

ELECTROMECHANIGAL CALCULATOR Filed Oc t. 29, 1942 :5 Sheets-Sheet 5 IN VEN TOR.

Mam BY 9mm M M Patented Apr. 1, 1947 UNITED STATES TENT GFFRCE 8 Claims.

My invention relates in general to an electromechanical mechanism forsolving equations which may be solved vectorially and more particularlyto an electro-mechanical directional antenna pattern calculator.

While I will describe my invention as being embodied in anelectro-mechanical directional antenna pattern calculator, yet it is tobe understood that my invention may be embodied in other forms to solveother problems of a similar or varied nature.

The outstanding problem in antenna design is always to control thedistribution of the radiated energy in some desired manner. Theradiation pattern or Space characteristic, is a geometrical descriptionof the manner in which the radiant energy is distributed in space aroundthe radiators or antennas. The horizontal pattern represents thedistribution in the ground plane, and the various vertical planepatterns represent conditions in directions at various angles above thehorizontal. The patterns are represented in polar graphs and may bedrawn in terms of relative or actual field strength or power. Thepresent description will be in terms of relative field intensities.

The field intensity in any direction from one or more antennas whichradiate power at the same frequency can be calculated from a standardequation, provided sufiicient conditions are known concerning theantennas, their arrangement and the distribution of power to them. Thegroup of antennas used to radiate power is spoken of as the antennaarray. The greater the number of antennas in an array, the more time andwork is required to calculate the radiation pattern for that array. Inorder to design an array of antennas to give a definite desired pattern,it is often necessary to determine, by trial, the radiation pattern forseveral arrays before the correct array is selected. Consequently, agreat amount of time and eliort is entailed in the design of an antennaarray forthe purpose of getting a desired field'intensity pattern.

In the design of an antenna array, it is electrically possible to mouldthe radiation pattern in almost any desired manner. As the number ofradiators or antennas is increased, a greater degree of control becomespossible. Y

- The general equation for the field intensity from a directionalantenna array of any number of antennas, n, is:

Equation 1 may be written in vector form as follows:

Each of the terms in the right hand side of Equation 2 may be expandedaccording to the Equation 1, as is shown in the following equation forthe 70th antenna only:

The several factors in the right hand side of Equation 3, are defined asfollows:

Ek=the horizontal magnitude of the field intensity produced by the kthantenna.

me) =vertical radiation characteristic of the kth antenna having unityvalue along the horizon. In my invention this characteristic can haveany desired shape.

e lc=a unit vector that determines the direction of the vectorrepresenting the field from the kth antenna.

cos (it;, sin 6) cos h fkw- (l-cos h cos 6 (4) Equation 4 is for thespecial case of a vertical antenna having sinusoidal currentdistribution with a current node at the top.

e k=cos B A-j sin 6 1 1F 1. cos (ck-o) cos h.

The nomenclature used is 45 0=e1evation angle of observation point, p,from the horizontal in degrees h1 =electrical height of kth antenna indegrees S1 =electrica1 spacing of Icth antenna from a space referencepoint in degrees. i =horizontal azimuth orientation angle of lathantenna with respect to a space reference axis. =horizontal azimuthangle of the direction to the observation point, p. b1 =electrical phaseangle ofthe field radiated from the kth antenna with respect to thephase angle of a field radiated from the space refe rence point.

i=\/-1, imaginary operator.

e=2.718, the base of natural logarithms By use of Equations 4, 5 and 6,Equation 3 may be written in component form to make Equation '7;

cos (h sin )cos h (lcos h cos 0 1 t cos (k 00s +d+ 1' sin t cos (k cos+E k] l h (7) For several antennas, the components as given in Equation'7 for one antenna may be added and the resultant vector written itherin component vector form or combined to give the magnitude of theresultant field.

The description will deal with a four-element array, but it is to beunderstood that my invention may be applied to any number of elements.For a four-element antenna array, the following equation is accepted asa standard for calculating the relative field intensity in anydirection, both horizontally and Vertically.

The magnitude of the resultant field intensity, represented by E, for afour element array, having individual antennas of unequal height, is:

of an electro-mechanical mechanism adapted to solve equations which maybe represented by the general vector equation,

hereinafter referred to.

Another object of my invention is the provision of an electro-mechanicalmechanism which will solve for the value of the radical expressed in theEquations 8 and 9 above.

Another object of my invention is the provision of an electro-mechanicalmechanism for generating a movement corresponding to a cosine functionand for transferring the said movement to the rotation of electricalequipment producing electrical conditions which combine to give aresultant electrical condition which may be read directly at anyposition throughout the complete cycle of the generated movement.

Another object of my invention is the provision of an electro-mechanicalmechanism for generating a movement correspondin to a cosine functionand for transferring the said movement to modify a plurality ofelectrical conditions which when affected by the generated movementprovide for giving a resultant electrical condition at any positionthroughout the complete cycle of the generated movement.

E: cos (k sin til-cos h,

i (1cos h cos 0 cos (h; sin 0)-cos ho (1-cos h cos 0 cos (in sin 0)-c0sh (1-c0s h cos 0 cos (h, sin Ol-cos h (l-cos In) cos 0 cos (h, sin0)--cos h S a L h!) c059 1s 1 s 1 d) 008 +1 1] cos (hg sin 0) cos k(1cos h cos 0 cos (h sin 0) --cos h (1-cos k cos 0 cos (h sin 0) cos it;(1-cos k cos 0 When the antenna heights are equal, Equation 8 simplifiesto:

E sin [S cos (ch-qt) 10 H-NF E3 sin 3 cos (3) 008 1 3] Another object ofmy invention is the provision of an electro-mechanical mechanism forgeneratcos (h sin 0) cos it (lcos h) cos 0 solve equations which may berepresented by the general vector quation,

ing recurrent movement and for transferring the said movement to modifya plurality of electrical conditions which when affected by thegenerated movement provide for giving a resultant electrical conditionat any position throughout the complete cycle of the generated movement.

Another object of my invention is the provision to specify independentlythe polarization and radiation characteristic of each element in theantenna array.

Another object of my invention is the provision of varying thegenerating recurrent motion as to Another object of my invention is theprovision amplitude and phase.

'Another object of my invention is the provision for adjusting themagnitude and Phase relation of an electrical condition with respect toa reference electrical condition.

Another object of my invention is the provision of an electro-mechanicalmechanism adapted to facilitate the calculation of the relative fieldintensity of two or more antenna elements in any direction, bothhorizontally and vertically.

Other objects and a fuller understanding of my invention may be had byreferring to the following description and claims, taken in conjunctionwith the accompanying drawings, in which: Figure 1 is a diagrammaticillustration of an electro-mechanical antenna array pattern calculatorembodying features of my invention;

Figure 2 is a plan view of a four element antenna array as actuallyinstalled in service, being an example of an installation for which mycalculator can be used to determine both the vertical and horizontalpatterns;

, Figure 3 is a representation in a horizontal plan view of the positionof the equivalent fourelement antenna array as shown in Figure 2 whenset ofi on my machine with a common reference point and with a commonreference axis for solving for one value of the field in the horizontalpattern where the angle equals zero;

. Figure 4 is a representation of the magnitude and the angle of thevoltage vectors representing the conditions in the component parts ofthe machine, as obtained by the setting of the machine for thearrangement in Figure 3, which vectors when vectorially added give aresultant vector that represents a function of the value of the fieldintensity being solved, where the angle equals zero;

Figure 5 is a representation similar to Figure 3 for solving for anothervalue of the field in the horizontal pattern, with the four-elementantenna array rotated through an angle of =320;

Figure 6 is a vector representation similar to Figure 4 as obtained bythe setting of the machine for the arrangement in Figure 5 for solvingfor another value of the field of the horizontal pattern wher the angle=320;

Figure '7 is a polar diagram of a horizontal radiation pattern of thefour-element antenna array as recorded by my pattern calculator, theresultant relative field for the settings in Figures 3 and 5 being shownat angles of 0 and 320 respectively;

Figure 8 is similar to Figure '7 but shows in addition, elevationalfield intensity patterns for elevational angles of 0=30 and 6:60";

Figure 9 is a reference chart used in the setting of the machine andshows the relation between the antenna height in degrees and f (0) inper cent of the value along the horizon for various elevation angles of0;,

Figure 10 is a representation similar to Figure 6 with the four-elementantenna array rotated through an angle of =320, being a representationof the electrical vectors corresponding to a setting of my machineutilized in solving for one elevational angle 0=30;

Figure 11 is a view similar to Figure 10, but is based upon anelevational angle 0:60"; and

Figure 12 is a vertical pattern at =320, when all antennas are 120 inheight.

The Equations 8 and 9 above for a four-element array are derived fromthe vector addition of cos (it sin 0) cos h (1-cos h) cos 0 the fourvectors which represent the strength of the signal from each of the fourantennas arriving at a common point far removed from the antenna array.Each of the four vectors is dependent only on the radiation from itsrespective antenna with respect to the reference point or origin. Astudy of these vectors and their relationship with each other will nowbe developed, in conjunction with Figure 3 of the drawings, whichdiagrammatically illustrates a fourelement array in an equivalenthorizontal plan view, as set oif on my machine in Figure 1.

Antenna No. 1 is chosen as the reference point or origin 0, and the line20 in the direction of angle =zero degrees, establishes a directionalreference line. Antenna No. 2 is spaced S2 degrees from antenna No. 1 ina direction 2 degrees from antenna No. 1 or from the reference line =0,drawn through No. 1. Antenna No. 3 is spaced S3 degrees from antenna No.1 at an angle of 3 degrees from the reference line for antenna No. 1.Antenna No. 4 is spaced S4 degrees from antenna No. 1 in a direction ordegrees from the reference line for antenna No. 1. The current inantenna No. 1 is assumed to have a phase of zero degrees, while that ofantenna No. 2 is in degrees, that of antenna No. 3 is 1,03 degrees andthat of No. 4 is m degrees with respect to antenna No. 1. The point ofobservation P may be considered to be anywhere on a circle drawn fromthe origin 0, and it is assumed that the distance from the point ofobservation to the array is great enough that lines E1, E2, E3, and E4representing the fields respectively for the four antennas, drawn from Oto P, No. 2 to P, No. 3 to P, and No. 4 to P are for all practicalpurposes parallel Where P lies in a direction, =320. It is furtherassumed (for simplification) that the observation point P is an integralnumber of wave-lengths from O, which means that the signal from antennaNo. 1 is in time phase with the current in antenna No. 1. Thus, thevector representing the signal from antenna No. 1, being a referencevector, may be drawn at an angle of zero degrees and its length willdepend upon the strength of the signal from antenna No. 1. Antenna No. 2is farther away from P than antenna No. 1 by a magnitude, S2 cos (4 2-)degrees. As a result, the signal from antenna No. 2 will arrive at Pbehind the signal from antenna No. 1 due to the longer path. The delayedarrival of the signal from antenna No. 2 to P due to the longer path iscompensated for or overcome by reason of the fact that the signal fromantenna No. 2 starts with phase 4/2 degrees ahead of signal from antennaNo. l. The combination of space and phase results in an equivalent phaseof, S2 cos (2 +il z degrees by which the signal from antenna No. 2arrives with reference to the signal from antenna No. l at theobservation point P. By a similar analysis, the signal from antenna No.3 arrives with reference to the signal from antenna No. 1 at theobservation point P by an equivalent phase of, S3 cos (3) +4 3 degreesand the signal from antenna No. 4 arrives with reference to the signalfrom antenna No. 1 at the observation point P by an equivalent phase of,S4 cos (4) 114 degrees.

For the horizontal pattern only since =0 Equation 10 may be expressed asfollows:

For a complete picture of the field pattern for an array, such as forexample the pattern shown in Figure 7, the total field must be found forP, a number of times and Where P is located at a different angle for thearray each time. Usually the field is calculated for P located atintervals of or degrees or any other value throughout the horizontalplane. That is to say, the point P in Figure 2, being a point at whichthe field intensity is determined, is but one of several points locatedradially about the origin 0 for the four antennas Nos. 1, 2, 3, and 4.In the actual field layout, the antennas remain fixed and theobservation point is moved in a clockwise direction about the origin ofthe array.

The embodiment of my invention as shown in Figure l is designed todetermine the field pattern for a four-element array. It can like-wisebe used directly for a two or three-element array. The principle may bealso extended to apply to more than four elements. Although the deviceoperates to solve radiation problems, its use is not limited to theirsolution only. It may be easily adapted to the solution of problems notrelated to radiation, Which involve functions equivalent to those foundin the equation for field intensity for antenna arrays or to those whichmay be solved vectorially. With particular reference to Figure 1, myelectro-mechanical directional antenna pattern calculator comprisesgenerally four main parts, namely a polar graphing turn table 2!, aplurality of cosine generator units 22, an electrical vector system 23,and a resultant vector responsive device 24. My electro-mechanicalcalculator accomplishes its purpose by starting with a simple mechanicalsystem, converting to an electrical system for flexibility, and finallyconverting back to a mechanical system to draw the field intensitypattern.

The polar graphing turn table 2| comprises a revolving plate 25 which isarranged to rotate around a pivot indicated by the reference characterA1 which also represents the location of antenna No. 1. Ihe revolvingplate 25 may be driven by a motor 28 through any suitable driving meansindicated generally by the dash-dot line 29. Around the peripheral edgeof the revolving plate 25 is a graduated degree scale indicated by thereference character 35 and may be designated as the o scale whichindicates the direction of the field as measured at the fixed arrowmarked P which is placed adjacent to the revolving plate 25. The graphpaper indicated by the reference character 21 may be removably mountedon the revolving plate 25 upon which the field intensity curve may bedrawn by means of an inking device 3| driven by a motor 32 which isenergized from the electrical supply conductor 33 and from the resultantvector responsive device 24. As the revolving plate 25 is rotated in acounter-clockwise direction as indicated by the arrow, the fieldintensity curve is automatically drawn upon the graph paper 21 by meansof the inking device 3| which is actuated radially by the motor 32. Thecurve as drawn upon the graph paper 21 is of substantially the samecontour as the curve shown in Figure 7 of the drawing. A planimeter 34may be actuated by the part Which moves the inking device 3| to measurethe area bounded by the curve from which the R. M. S. value of the fieldmay be readily computed. After the R. M. S. value is computed, theinking device 3| is set at a distance from the origin A1 which is ameasure of the R. M. S. value and then the turntable is rotated fordrawing the circle 35 which has a radius that is a measure of the R. M.S. value and whose area defined by the circle is equal to the areabounded by the field intensity pattern.

The cosine generator units designated generally by the referencecharacter 22 comprise three units 38, 39, and 40. Inasmuch as themechanical construction of the cosine generator units are substantiallyalike, the description will be devoted primarily to the cosine generator38 in order to prevent a duplication of the description. The cosinegenerator 38 comprises an orientation dial plate 4| which is pivotallymounted upon a pivot point indicated by the reference character A1 whichdesignates the position of the antenna N0. 1. A spacing arm 44 isactuated by the orientation dial plate 4| for driving a motiontransmitting means 49 which comprises a cross-member 5| that actuates arack member 54 which engages a pinion gear 55. The outer end of thespacing arm 44 is provided with a driving pin indicated by the referencecharacter A2 which indicates the location of the antenna No. 2 withreference to the antenna No. 1 located at the origin of the orientationdial plate 4|. The driving pin A2 is arranged to slidably engage a slot50 in the cross-member 5| which when the spacing arm 44 revolves causesthe rack member 54 to reciprocate and rotate the pinion gear 55. Thespacing arm 4 is arranged to pass through a clamping arrangement locatedat the center of the orientation dial plate 4| so that the length of thespacing arm may be adjusted by first unloosening an adjusting knob 45after which the spacing arm may be shifted radially to adjustablyposition the 10- cat-ion of the driving pin A2 with reference to theorigin A1, which spacing arm 44 has a scale thereon graduated inelectrical degrees. The orientation dial plate 4| may be driven by anysuitable mechanical means illustrated by the reference character 48 fromthe polar graphing turntable 2|, so that the orientation dial plate 4|rotates in unison with the polar graphing turntable 2| as indicated bythe arrow mark. Around the periphery of the orientation dial plate 4| isa graduated degree scale indicated by the reference character 4'! whichis the ig scale that indicates the orientation of the antenna No. 2. Theangular rotation of the orientation dial plate 4| which carries thespacing arm 44 may be shifted with respect to the polar graphingturntable 2| by means of clutch screws 45 which when loosened permit theoperator to swingably vary the angular position of the spacing arm 44with respect to the polar graphing turntable 2|. When the spacing arm 44is properly positioned, the clutch screws 46 may be again retightened sothat the spacing arm 44 is driven mechanically in unison with the polargraphing turn table 2|.

A driving pin A3 carried upon the free end of the spacing arm for thecosine generator unit 39 represents the position of the antenna N0. 3with respect to the origin which is the location of the antenna No. 1.Similarly, for the cosine generator unit 49, the driving pin A4designates the location of the antenna No. 4 with reference to theorigin which designates the location of the antenna No. 1. The angularposition represented by 2 is read upon the graduated degree scale on theorientation dial plate 4| at the fixed arrow mark z which is fixed tothe machine. By the same arrangement, the orientation dial plates 42 and43 for the cosine generator 39 and 49, respectively, may also carrygraduated degree scales whereby the angular position of the spacing armswhich carry the driving pins A3 and A4 may be observed with reference tothe fixed arrow points 3 and 54 carried by the machine and locatedadjacent to the peripheral edge of the orientation dial plates 42 and43, respectively. The orientation dial plates 42 and 53 are likewisedriven in unison through any suitable means from the revolving plate 25of the polar graphing turntable 2|. The spacing arms for the cosinegenerators 39 and il] may be adjustably set both angularly and radiallythe same as that described with reference to the cosine generator 38.

The pinion gear 55 which is actuated by the cosine generator 38 isarranged to drive an armature BI of a phase shifting transformer havinga field 62 energized by a three-phase supply source indicated by theconductors 53, 54, and 65. The

phase shifting transformer may be of any suitable type, several of whichare available commercially. I have chosen to depict an electromechanicaldevice physically similar to selsyn or autosyn,

which comprises a three phase stator used as a primary in thisapplication, and a single phase wound rotor used as a secondary in thisapplication. As the angular position of the rotor is varied, the phaseof the voltage produced therein is varied with respect to any phase ofthe three phase stator. A phase clutch 55 is positioned between thepinion gear 55 and the armature GI of the phase shifting transformer sothat the angular position of the armature 5| may be shifted with respectto the pinion gear 55 which has a fixed position with reference to therevolving plate 25 of the polar graphing turntable 2|. Asdiagrammatically shown, the phase clutch 56 comprises two relativelycircular movable parts releasably clamped together by means of anadjusting knob 59. The inner circular part 56 is driven by the piniongear 55 and the outer circular part 57 is arranged to drive the armature6! of the phase shifting transformer. The outer circular part 51 of thephase clutch 55 carries a graduated scale 5'! which when observed Withreference to the arrow carried by the inner circle and indicated by &2gives the time phase relation of 1/2 wherever it may appear in theequation being solved. The graduated scale 51 with reference to thestatic-nary mark 182 gives the angular position of the armature 9| ofthe phase shifting transformer and takes care of the factor 182 in theequations which are to be solved. The voltage output of the armature 5|is impressed across an adjustable resistor 61 which is of thepotentiometer type and which has a slidable pointer 68 to give an outputvoltage which may be adjustably varied by the operator. The value of thevoltage given by the adjustable or slidable pointer 58 is a measure ofthe voltage E2 on the horizontal pattern. The voltage given by theslidable pointer 58 is impressed across an adjustable resistor 69 whichis also of the potentiometer type and has a slidable pointer Ill. Theslidable pointer 19 10 gives a variable voltage which compensates forthe field at the various elevational angles, 0. The voltage given by theadjustable pointer I9 is impressed across 3. volt meter 83 which givesthe magnitude of the voltage E2. The length of the arrow passing throughthe voltmeter B3 is proportional to the magnitude of the voltage and theangle of the arrow represents the angle 52 as observed upon the phaseclutch 55 positioned between the pinion gear 55 and the armature GI ofthe phase shifting transformer. The electrical parts associated with thearmature 6| of the phase shiftin transformer may be designated generallyas an electrical vector unit and is indicated by the reference character16. The electrical vector unit I6 takes care of the factors involvingthe antenna No. 2. Similarly, the electrical vector units I1 and 78 takecare of the electrical conditions involving the antennas No. 3 and No.4, respectively. The electrical vector unit 11 and I8 are the samegeneral construction as that shown and described for the electricalvector unit it. The electrical vector unit 1! has an adjustable resistor81 of the potentiometer type across the armature of the phase shiftingtransformer and thc slidable pointer 88 thereon gives a voltage that isthe measure of E3 on the horizontal pattern. The adjustable resistor 89which is of the potentiometer type and which has a pointer 90 isarranged to give a voltage which compensates for the field at thevarious elevational angles, 0. Similarly, for the electrical vector unit78, the adjustable resistor 9| is connected across the armature of thephase shifting transformer and the slidable pointer 92 thereon providesfor giving a voltage which is a measure of E4 on the horizontal pattern.The field at the various elevational angles of 0 is compensated for bythe adjustable resistor 93 having a pointer 9 The voltmeters 84 and 95,respectively. read the value for E3 and E4. The arrow which passesthrough the voltmeter 84 is proportional to the magnitude of the voltageE3 and the angle is a measurement of B3. The arrow which passes throughthe voltmeter 85 has a magnitude that is proportional to the voltage E4and the angle is a measurement of 54 in the equation to be solved. Theelectrical vector unit designated by the reference character I5 isarranged to be energized from the three-phase supply conductors 64 and55 and comprises a potentiometer resistor 95 which has a slidablepointer 96 that gives a voltage which is a measurement of E1 on thehorizontal pattern. The field at various elevational angles of 6 iscompensated for by the potentiometer resistor 91 having a slidablepointer 98 which is connected to the voltmeter 82 that reads the valueof E1. The arrow which passes through the voltmeter 82 has a lengthwhich is a function of the magnitude of the voltage E1 and the angle ofthe arrow with respect to the horizontal represents 1 which is zerodegrees. The output of the electrical vector units I5, 16, TI, and I8are connected in series and the resultant voltage is read by a resultantvoltmeter 86. The circuit which connects the electrical vector units inseries to give the resultant voltage may be traced as follows: beginningwith the conductor I09 which is connected to one side of the resultantvoltmeter 85 the circuit extends through the voltmeter 82, conductorsI0l and 99, a switch I02, the voltmeter 85, switche I93 and I05, thevoltmeter 84, switches I95 and IE6, the voltmeter 83, a switch I01 and aconductor I98 to the other side of the resultant voltmeter 86. Theresultant voltage is impressed degrees.

upon the resultant vector responsive device 24 which may be a poweramplifying device which supplies current to the motor 32 that drives theinking device 3! for making the graph of the field intensity patternupon the graph paper 21 of the polar graphing turntable 2|. Thedirection of rotation of the motor 32 is determined by the resultantvector responsive device 24 to radially operate the inking device 3| onthe graph paper as it is revolved by the polar graphing turntable 2|.

In explaining the operation of my electro-mechanical antenna patterncalculator, let it be assumed that the antenna heights are all equal to120 degrees and that the value of the relative field intensity, E, is tobe calculated for the horizontal pattern under the following prevailingconditions, in which:

The physical location of the four elementary antenna-array for the aboveset of values is shown in Figure 2, where 2=180, 3=80, and 4=230;S2=180, S3=1l0, and 54:200"; z=240, 3=130, and b4=30; and E1, E2, E3,and E4 equal 1.0, 1.25. 1.75, and 1.5 respectively.

Before setting the values off on my machine the revolving plate 25 ofthe polar graphing turntable 2| is locked by actuating the cam lock 36against the peripheral edge of the revolving plate 25, to make the scale30 read zero for making all of the orientation adjustments. Theorientation angle 2 for the antenna No. 2 is set off on the orientationdial plate 41 of the cosine generator unit 38 to make the graduatedscale read 180 This may be done by operating the orientation clutchscrews 46. Similarly, the orientation angle 3 is set oil at 80 degreeson the orientation dial plate 42 for the cosine generator unit 39 andthe orientation angle m is set oil at 230 degrees on the orientationdial plate 43 of the cosine generator unit 49. After the orientationangles are once set ofi on the cosine generator units 38, 39, and G0,the revolving plate 25 may be unlocked by operating the cam lock 36 tothe release position. The antenna spacing S2 is set off on the cosinegenerator unit 38 by making the spacing arm 44 read 180 degrees betweenA1 and A2. Similarly, the antenna spacings S3 and S; are set off,respectively, on the cosine generator units 39 and 40 by making thespacing between A1 and A3 read 110 degrees and the spacing between A1and A4 read 200 degrees. If the orientation dial plates M, 42, and 43together with their spacing arms were placed vertically above each otherand also placed above the turntable 2|, the combined showing of thespacings for all of the antennas and their angular positions withrespect to each other would be the same as that diagrammaticallyillustrated in Figure 3 which may be considered as an equivalentmechanical arrangement ,1 of the array shown in Figure 2. In my cosinegenerator arrangement, which i diagrammatically illustrated in Figure 3,the angles iz, oz, and 54 are measured in a counter-clockwise directionwhereas in Figure 2 which represents the actual field location of theantenna, the angles 2, 3 414 are measured in clockwise direction. Thereason for this is that, in

the field, the observer at the point P is considered as moving bodily ina circle around the origin of the antennas, whereas in my machine theobserver is considered as remaining stationary and the antennas A2, A3and A4 are' rotated bodily about the antenna A1 as the origin. The timephase angle he is set off on the phase clutch 56 by operating theadjusting knob 6i and moving the two relatively movable parts of theclutch mi:- til the graduated scale 51 reads 240 degrees with respect tothe arrow designated as a, after which the knob 60 is tightened to keepthe two parts of the clutch anchored together for operating the armature6| of the phase shifting transformer. In the same manner, the time phasefactors he and !/4 are set oii at 130 and 30, respectively, on theclutches which operate the armature of the electrical vector units 11and '18. respectively. The pointers 98, T5, 90, and 94 for thepotentiometer resistors 91, 69, 89, and 93, respectively, whichcompensate for the field at the various elevational angles are set attheir maximum value since the machine is now being described forproducing the horizontal pattern. After the pointers 98, 10, 90 and 9 3are once set for the horizontal position, the adjustable pointers 96,68, 88, and 32 for the potentiometer 95, 67, 81, and 9| are so shiftedto make the voltmeters 82, 83, 84, and to read, respectively, 1.0, 1.25,1.75, and 1.5, which are the values for E1, E2, E3 and E4 respectively.The machine is now all set for producing the graph of the fieldintensity for the horizontal pattern on the revolving plate 25 of thepolar graphing turntable 2|. Prior to starting the machine, a sheet ofgraph paper 2'! is arranged on the revolving plate 25 after which theinking device 3! is set on the paper and the planimeter 34 is set tozero. The motor 28 is now started and drives the revolving plate 25through one complete cycle of 360 degrees which gives a graphsubstantially as shown in Figures 1 and 7 of the drawing, the Figure 7being shown inverted to correspond to the actual condition in the fieldas shown by Figure 2. A clutch may be mounted between the motor 28 andthe revolving plate 25 so that the turntable may be revolved by handwhen desired. To determine the R. M. S. value for the horizontalpattern, the planimeter is read and from this reading computations maybe readily made for determining the R. M. S. value for the field. Theinking device 3| may then be set at a fixed distance away from theorigin A1 to equal the computed R. M. S. value, whereupon the revolvingplate 25 may be rotated through a complete cycle of 360 degrees fordrawing the circle 35 which has an area equivalent to the area boundedby the horizontal pattern drawn by the inking device 3! when the machineis operated. The Figure 4 is a vector diagram illustrating the voltagemagnitudes and the voltage angles of the electrical vector units 15, 16,11 and 18 for the condition that equals zero as set off on the revolvingplate 25 of the polar graph turntable 2|. The Figure 6 is similar toFigure 4 and shows the voltage magnitudes and angles of the electricalvector units l5, '16, 'l'! and 18 when the direction angle is 320degrees as shown in Figure 5.

The angles for Ba, [33, and at for constructing the vector diagrams inFigures 4 and 6 may be directly read off the machine at the phaseclutches between the pinion gears and the armatures of the phaseshifting transformers. The p angles for any other value of i may bedetermined in the same manner.

Besides the horizontal pattern, my machine may be used for determiningthe vertical pattern for any horizontal direction of When using mymachine to determine the vertical pattern, I preferably employ thefollowing procedure: First I draw the horizontal pattern as previouslyexplained and then I draw a series of other patterns at variouselevational angles. In Figure 8, I show the horizontal pattern as beingindicated 13 by the reference character H0, a second pattern by thereference III and a third pattern by the reference character H2. Thesecond pattern is taken for the elevational angle equals 30 degrees andthe third pattern H2 is taken at the elevational angle 8 equals 60degrees. While I have drawn only two elevational patterns at 30 and 60degrees, it is to be understood that any number of patterns may be drawnat the angle between the horizontal and 90 degrees. In drawing theadditional patterns as shown on Figure 8, I shift the location of thepointers 98, Ill, 90 and 94 .along their respective potentiometerresistors to compensate for the field at the various elevational angles.In determining the actual position of the compensating pointers, I havedeveloped a readily usable chart as shown in Figure 9 which enables meto set the pointers off to compensate for the field at the variouselevational angles with ease. The chart in Figure 9 shows therelationship between the antenna heights in degrees to m) in per centwhich is the elevationa1 compensating factor. Thus, for example, for anantenna height of 120 degrees and for an elevational angle of 30 thecompensating factor is approximately 78 per cent times the value of thesetting of the pointers for the horizontal pattern. In other words, thesecond pattern I I I is compressed radially to approximately '78 percent of the horizontal pattern III). For the third pattern H2 which istaken at an elevational angle of 60 the compensation for the setting ofthepointers is approximately 34 per cent of the value for the setting atthe horizontal pattern. By the use of the chart in Figure 9 any numberof patterns may be drawn. In addition to compensating for the positionof the pointers for the potentiometer resistors 91, 69, 89 and 93, Ialso compensate for the apparent spacing between the antenna No. 1 atthe origin and the antennas Nos. 2, 3, and 4 by shifting the length ofthe swinging arms of the cosine generator units 38, 39, and 40. In otherwords, as the observation point P increases in elevation, the distancesto the respective antennas gradually approach each other in value andbecome equal at 0:90 degrees, which means that the apparent spacingbetween the antennas becomes zero. The changes in spacing from theantenna A1 at the origin and the antennas A2, A3, and A4 at the end ofthe swinging arms in the cosine generators is computed from the cosinefunction of the elevational angle at which the pattern is being drawn.After the potentiometer pointers are reset to compensate for the variouselevational angles and after the spacings are set upon the cosinegenerators, the machine is ready to draw an additional pattern taken atthe selected elevational angle 0. The vertical pattern in Figure 12 istaken for a value equal to 320 degrees and the values for determiningthe contour of the vertical pattern may be measured directly on onFigure 8 taken along the radial line marked 32!! which has been drawnheavier than the other line. The points H5, I I6, and I I! where theradial line 320 crosses the three patterns IIEI, III, and H2, give theradial lengths at which the corresponding points are determined for thevertical pattern in Figure 12. The distance from the origin in Figure 8out to the point I I5 represents the value of E at an elevation angle of0:0 degrees and is shown by the resultant line E in Figure 6. Thedistance from the origin in Figure 8 out to the point I I6 representsthe value of E at an elevational angle of 0:30 degrees and is shown bythe resultant line E in Figure 10.

The Figure 11 is similar to Figure 10 but shows the resultant for anelevational angle 0:60 degrees and the resultant line E is the same asthe distance from the origin to the point I II in Figure The verticalpattern may be drawn for any other value of c by determining the radialdistances from the origin of the graph in Figure 8 to the points wherethe radial angle of intersects the respective patterns taken at thevarious elevational angles of 0. The Figures 7, 8, and 12 are drawnone-half scale with respect to Figures 4, 6, 10, and 11.

While I have described my invention as being designed for the solving ofthe antenna patterns for a four element array, it is to be understoodthat the invention may be changed to cover more or less than a fourelement array, for example, any one of the electrical vector units suchas, for example, I8 may be rendered inoperative and removed from thesystem by throwing the switches IE2 and I63 to include the resistor I20in the circuit which substantially matches the resistance of theelectrical vector unit which was removed from the circuit. The resistorI20 enables the remaining electrical vector units I5, I6, and I? toremain operative as a thre element array. My invention may be used tosolve a two element array by excluding two of the electrical vectorunits such, for example, as TI and I8. In general an n element array canbe solved by adding (n-l) cosine generator units similar to the threeunits 38, 39, and II] which are-used for a four element array.

Although I have described my invention with a certain degree ofparticularity, it is understood that the present disclosure has beenmade only by way of example and that numerous changes in the details ofconstruction and the combination and arrangement of parts may beresorted to without departing from the spirit and the scope of theinvention as hereinafter claimed.

I claim as my invention:

1. An electro-mechanical antenna array pattern calculator, including aplurality of similar units and a reference unit, each of said similarunits containing two means, one for generating a variable voltage andone for adjusting said voltage, said generating means including arotative phase shifting element, and said adjusting means includingmechanism for rotating the phase shifting element in accordance with anadjustable cosine movement, a series electrical connection between thegenerating units and the reference unit, said reference unit containingmeans responsive to the sum of the generated voltages for indicating themagnitude and direction thereof.

2. A machine for vector summation of n vectors, comprising, 11. cosinegenerator units, means for driving said 11 cosine generator units insynchronism, n electrical vector systems each having electrical outputsand each being actuated by one of said cosine generator units,respectively, a potential source for energizing said electrical vectorsystems, a resultant vector responsive device having an electrical inputand being responsive to said n electrical vector systems, and means forserially connecting the outputs of said 72 electrical vector systems tothe input of said resultant vector responsive device, said n electricalvector systems each comprising electromechanical phase shift meanshaving a rotor and a stator, rotatably positionable phase clutch meansconnected between said rotor and said cosine generator unit, said rotorhaving an electrical output of variable phase, energization means for 15energizing said stator of said phase shift means from said potentialsource, and first and second electrical magnitude control means forcontrolling the magnitude of the electrical output of said phase shiftmeans.

3. A machine for vector summation of n vectors, comprising, n-l cosinegenerator units, means for driving said n-l cosine generator units insynchronism, 11-1 electrical vector systems each having electricaloutputs and each being actuated by one of said cosine generator units,respectively, reference means for establishing a reference vector ofvariable magnitude, a potential source for energizing said referencemeans, said reference means including first and second magnitude controlmeans for controlling the magnitude of the reference vector, a resultantvector responsive device having an electrical input and being responsiveto said n-l electrical vector systems and said reference vector toindicate the resultant thereof, and means for serially connecting theoutput of said n-1 electrical vector systems and the output of saidreference means to the input of said resultant vector responsive device,said n-1 electrical vector systems each comprising electromechanicalphase shift means having a rotor and a stator, rotatably positionablephase clutch means connected between said rotor and said cosinegenerator unit, said rotor having an electrical output of variablephase, energization means for energizing said stator of said phase shiftmeans from said potential source, and first and second electricalmagnitude control means for controlling the magnitude of the electricaloutput of said phase shift means.

4. A machine for vector summation of n vectors, comprising, n-l cosinegenerator units, means for driving said 11-l cosine generator units insynchronism, n-1 electrical vector systems each havingelectrical'outputs and each being actuated by one of said cosinegenerator units, respectively, reference means for establishing areference vector of variable magnitude, a potential source forenergizing said reference means, said reference means including firstand second magnitude control means for controlling the magnitude'of thereference vector, a resultant vector responsive device having anelectrical input and being responsive to said n-l electrical vectorsystems to indicate the resultant thereof, and means for seriallyconnecting the outputs of said n-l electrical vector systems and theoutput of said reference means to the input of said resultant vectorresponsive device, said n-l cosine generator units each comprisingrotatable means having a radially adjustable spacing arm thereon, meansfor varying the angular position of said rotatable means with respect toeach other, a reciprocating rack arm driven by said spacing arm, and apinion gear rotated by said rack arm, said n-l electrical vector systemseach comprising electromechanical phase shift means having a rotor and astator, rotatably positionable phase clutch means connected between saidrotor and said pinion gear, said rotor having an electrical output ofvariable phase, energization means for energizing said stator of saidphase shift means from said potential source, and first and secondelectrical magnitude control means for controlling the magnitude of theelectrical output of said phase shift means. 7

5. A machine for vector summation of n vectors, comprising a polargraphing turntable with a polar graph thereon, n-1 cosine generatorunits, means for driving said turntable and said 12-1 cosine generatorunits in synchronism, n-l electrical vector systems each havingelectrical outputs and each being actuated by one of said cosinegenerator units, respectively, reference means for establishing areference vector of variable magnitude, a potential source forenergizing said reference means, said reference means including firstand second magnitude control means for controlling the magnitude of thereference vector, a resultant vector responsive device having anelectrical input and output and being responsive to said n-1 electricalvector systems and said reference vector, means for serially connectingthe outputs of said n-1 electrical vector systems and the output of saidreference means to the input of said resultant vector responsive device,and recording means for translating said electrical output of saidresultant vector responsive device into a mechanical movement forrecording thereof on said polar graph, said n-l electrical vectorsystems each comprising electromechanical phase shift means having arotor and a tator, rotatably positionable phase clutch means connectedbetween said rotor and said cosine generator units, said rotor having anelectrical output of variable phase, energization means for energizingsaid stator of said phase shift means from said potential source, andfirst and second electrical magnitude control means for controlling themagnitude of the electrical output of said phase shift means.

6. A machine for vector summation of n vectors, comprising, a polargraphing turntable with a polar graph thereon, n-1 cosine generatorunits, means for driving said turntable and said n-l cosine generatorunits in synchronism, n1 electrical vector systems each havingelectrical outputs and each being actuated by one of said cosinegenerator units, respectively, reference means for establishing areference vector of variable magnitude, a potential source forenergizing said reference means, said reference means including firstand second magnitude control means for controlling the magnitude of thereference vector, a resultant vector responsive device having anelectrical input and output and being responsive to said n-1 electricalvector systems and said reference vector, means for serially connectingthe outputs of said n-l electrical vector systems and the output of saidreference means to the input of said resultant vector responsive device,and recording means for translating said electrical output of saidresultant vector responsive device into a mechanical movement forrecording thereof'on said polar graph, said n-1 cosine generator unitseach comprising rotatable means having a radially adjustable spacing armthereon, means for varying the angular position of said rotatable meansWith respect to said turntable, a reciprocating rack arm driven by saidspacing arm, and a pinion gear rotated by said rack arm, said n-lelectrical vector systems each comprising electric-mechanical phaseshift means having arotor and a stator, rotatably positionable phaseclutch means connected between said rotor and said pinion gear, saidrotor having an electrical output of variable phase, energization meansfor energizing said stator of said phase shift means from said potentialsource, andfirst and second electrical magnitude control means forcontrolling the magnitude of the electrical output of said phase shiftmeans.

'7. A machine for producing a resultant vector condition from aplurality of individual vector conditions comprising, in combination, aplurality of means comprising at least first, second and third meansestablishing respectively first, second and third individual vectorconditions, means for varying the relative magnitudes of the said vectorconditions, said means including phase rotating elements for varying therelative phase of each of said plurality of means, first, second andthird adjustable cosine generator units for generating movementscorresponding to an adjusted cosine function, means for transmitting thegenerated cosine movements to the respective phase rotating elements, aresultant vector responsive device, and connection means for connectingthe said plurality of means to the said resultant vector responsivedevice.

8. A machine for producing a resultant vector condition from a pluralityof individual vector conditions comprising, in combination, a, pluralityof means comprising at least first, second, third and fourth meansestablishing respectively first, second, third and fourth individualvector conditions, means for varying the relative magnitudes of the saidvector conditions, means including phase rotating elements for varyingthe relative phase of each but one of said plurality of means, first,second and third adjustable cosine generator units for generatingmovements corresponding to an adjusted cosine function, means fortransmitting the generated cosine movements to the respective phaserotating elements, a resultant vec- 18 tor responsive device, andconnection means for connecting the said plurality of means to the saidresultant vector responsive device.

CARL E. SMITH.

REFERENCES CITED The following references are of record in the file ofthis patent:

UNITED STATES PATENTS Number Name Date 1,559,325 Jewett Oct. 27, 19232,307,536 Parker Jan. 5, 1943 1,667,497 Shapiro Apr. 24, 1928 2,337,968Brown Dec. 28, 1943 FOREIGN PATENTS Number Country Date 400,714 BritishNov. 2, 1933 OTHER REFERENCES Maxwell, An Electrical Method forCompounding Sine Functions, R. S. 1., vol. 11, #2, Feb. 1940, page 4'7,Q184, R454.

Herr et al., An Electrical Algebraic Equation Solver, R. S. 1., vol. 9,Oct. 1938, pages 310 to 315.

Horizontal Polar Pattern Tracer, pages 227 to 232 of Proceedings of theI. R. E. for May 1942.

A Mechanical Calculator for Directional Antenna Patterns, pages 233 to237 of Proceedings of the I. R. E. for May 1942.

